Geometrical Interpretation of Complex Numbers (1 Viewer)

[Intilegience]

Can someone send working out for/explain this question:

The points A and B represent the complex numbers z1 and z2 respectively, where modulus of z1=1 and arg(z1)=theta

OB is root3 times as long as OA and <AOB = 90. B represents the complex number z2

Which complex number re[resents z2-z1?

 

[scaryshark09]

is the answer 2cis(theta - 2/3pi)

 

[Intilegience]

they gave it in euler form as e^i(theta+ 2pi/3)

I also got modulus as 2

 

[liamkk112]

they gave it in euler form as e^i(theta+ 2pi/3)

I also got modulus as 2

there are two solutions. as <AOB = pi/2 then either z2 is a rotation of z1 anticlockwise by pi/2 or clockwise by pi/2, meaning arg(z2)= pi/2 + theta or arg(z2) = pi/2 - theta. hence there should be two solutions. pretty sure modulus is also two, that seems correct as |z2| = sqrt(3).

 

[Intilegience]

Thanks for your help